BZOJ 4802 欧拉函数（Pollard_Rho）

【题目链接】 http://www.lydsy.com/JudgeOnline/problem.php?id=4802

【题目大意】

　　已知N，求phi(N)，N<=10^18

【题解】

　　我们用Pollard_Rho对N进行质因数分解，然后计算欧拉函数即可。

【代码】

#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
#define C 2730
#define S 3
using namespace std;
typedef long long ll;
ll n,m,cnt,cnf,ans;
vector<ll> v;
ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
ll mul(ll a,ll b,ll n){return(a*b-(ll)(a/(long double)n*b+1e-3)*n+n)%n;}
ll pow(ll a, ll b, ll n){
    ll d=1; a%=n;
    while(b){
        if(b&1)d=mul(d,a,n);
        a=mul(a,a,n);
        b>>=1;
    }return d;
}
bool check(ll a,ll n){
    ll m=n-1,x,y;int i,j=0;
    while(!(m&1))m>>=1,j++;
    x=pow(a,m,n);
    for(i=1;i<=j;x=y,i++){
        y=pow(x,2,n);
        if((y==1)&&(x!=1)&&(x!=n-1))return 1;
    }return y!=1;
}
bool miller_rabin(int times,ll n){
    ll a;
    if(n==1)return 0;
    if(n==2)return 1;
    if(!(n&1))return 0;
    while(times--)if(check(rand()%(n-1)+1,n))return 0;
    return 1;
}
ll pollard_rho(ll n,int c){
    ll i=1,k=2,x=rand()%n,y=x,d;
    while(1){
        i++,x=(mul(x,x,n)+c)%n,d=gcd(y-x,n);
        if(d>1&&d<n)return d;
        if(y==x)return n;
        if(i==k)y=x,k<<=1;
    }
}
void findfac(ll n,int c){
    if(n==1)return;
    if(miller_rabin(S,n)){
        v.push_back(n);
        return;
    }ll m=n;
    while(m==n)m=pollard_rho(n,c--);
    findfac(m,c),findfac(n/m,c);
}
int main(){
    while(~scanf("%lld",&n)){
        findfac(n,C);
        sort(v.begin(),v.end());
        v.erase(unique(v.begin(),v.end()),v.end());
        ll phi=n;
        for(int i=0;i<v.size();i++){
            ll y=v[i];
            phi=(phi/y)*(y-1);
        }printf("%lld\n",phi);
    }return 0;
}